Mikio Sato Collected Papers Volume III

Mikio Sato (1928 2023) is one of the most original and influential mathematicians of the twentieth century, whose ideas continue to shape modern mathematics. He initiates the theories of hyperfunctions and D-modules, laying the foundations of what he later called algebraic analysis. These innovations establish a unifying framework for analysis, algebra, and geometry, while revealing deep connections with theoretical physics. His work profoundly influences developments in analysis, number theory, holonomic quantum field theory, and integrable systems.

This three-volume collected edition presents a representative and authoritative selection of Sato s writings, reflecting both the breadth of his vision and the coherence of his thought. Volume I focuses on algebraic analysis, especially hyperfunction theory and microlocal analysis. Volume II centers on mathematical physics, notably holonomic quantum field theory. Volume III gathers works on prehomogeneous vector spaces, number theory, exact WKB analysis, and integrable systems, including soliton equations, highlighting the unity of Sato s mathematics across diverse domains.

Each volume opens with substantial scholarly commentaries by leading experts. These commentaries place Sato s work in historical and intellectual context, clarify the state of the subject before his contributions, and elucidate his conceptual innovations. Together, they comprise over one hundred pages of critical assessment and reflection, offering insight into the enduring impact of Sato s ideas on later developments.

To document the full scope of his research and influence, the edition includes a comprehensive bibliography encompassing informal materials not reproduced in these volumes.

This collection stands as both a definitive record of Sato s achievements and an enduring source of inspiration, demonstrating how bold conceptual thinking can open new directions in mathematics and providing a model for future generations.